Multiplying with Decimals Day 2

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Objective

SWBAT: • Make estimates of multiplication problems involving decimals • Multiply multi-digit decimals together

Big Idea

If 24 x 63 =1512, then what will be the product for 0.24 x 6.3? Students work on answering these questions and solidifying an algorithm for multiplying decimals.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, I want students to connect their knowledge of multiplying whole numbers to multiplying with decimals.   I want students to recognize that 6 x 6 = 36 and that _____ x 6 = .36.  Hopefully they will realize that the missing factor needs to be smaller than 1.  It is okay for students to take a guess; we will be working on these skills throughout the lesson. 

I ask students to share out their answers and we talk about how they figured them out. Some students will use math facts.  Other students may use repeated addition, while others may use the algorithm.  

What about the decimal point? Part 2

10 minutes

A common struggle with students is that they do not know where the decimal point should go in their product.  We did a similar activity in the previous lesson (Multiplying with Decimals), so students should be used the to structure.  The first step is that they can estimate to see if their answer makes sense.  I Create Homogeneous Groups using data from the ticket to go from Multiplying with Decimals. 

I have a volunteer read the task and pass out the calculators.  I give students 2-5 minutes to make their estimates and calculate their answers.  I walk around to ensure that students are on tasks and write neatly. 

We come back together as a class.  I ask students to think about what patterns they notice in their answers and what questions they have.  I read the directions for “Comparing Sets” and explain that they will participate in a Think Write Pair ShareStudents are engaging in MP8: Look for and express regularity in repeated reasoning and MP3: Construct viable arguments and critique the reasoning of others.

Then I ask for volunteers to share out with the class.  What patterns did you and your partner notice?  I want students to see the relationship between the number of decimal places in the factors and the number of decimal places in the product.  As you move from x10 to x100, you move the decimal place one extra place to the right.  We test their ideas using the problems in Set A and Set B.

I have a volunteer collect the calculators.

24 x 63

5 minutes

I have students multiply 24 x 63 and share their answer (1512).  Here I want students to first make a reasonable estimate, then use the initial problem (24 x 63 = 1512) to figure out where the decimal point goes in 1 5 1 2.  We do the first problem together.  I ask students to share an estimate for 0.24 x 6.3.  Some students may say less than 6.3 because you are multiplying 6.3 by something smaller than one.  Other students may say that 0.24 is smaller than 0.5, or 1/2, so the answer must be less than 3, which is ½ of 6.  Then we look at 1 5 1 2 and where we think the decimal point will go.  I want students to recognize that it must be 1.512, because 0.1512 is too small and 15.12 is too big! 

This activity is helping students build on their number sense.  These skills will help students recognize when their products are not reasonable.  It will also help students see patterns and develop their own short cuts when multiplying with decimals.  Students are engaging in MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

1.2 x 0.05

10 minutes

Before flipping to this page, I ask students to estimate the product of 1.2 x 0.05.  If students struggle, I ask them if they think their answer will be bigger or smaller than 1.2 and why.  I have students share out their estimates.

Then, I ask students to look at the three problems and answer the questions.  I have students participate in a Think Write Pair Share.  After a couple minutes of thinking and writing independently, I prompt students to share with one another.

I want students to recognize that each problem is using a different strategy to find an answer.  I will ask the class which answer is correct.  I want students to explain that all of the answers are equivalent.  I will feign ignorance, and declare that they can’t be equal, look at answer A, 0.0600 is surely larger than .060 because it has more decimal places.  I call on students to share their answers.

I ask students, “Which strategy do you think works best for you?” and “Which strategy do you think is most efficient?”  I want students to recognize that Problem A changes 1.2 into 1.20 so that the decimal points are aligned – you do not need to do this, but if you do you will just need to do more work.  Problem C uses the strategy of connecting 12 x 5 = 60, and using that fact and knowledge of decimal points to figure out the answer.  It is important that students see the similarities and differences between the approaches.

Practice

20 minutes

We do number 1 and 2 together.  I ask students how they want to find the exact product.  I also show them the algorithm.  I stress that students need to use their number sense and the patterns they noticed earlier to decide if their final answer makes sense. 

Students work independently on the rest of the problems.  They can check in with their partner if they are stuck.  I Poste A Key so that students can check their work when they finish a page.  I am looking that students are making reasonable estimates and that they are successfully multiplying the decimals using a strategy of their choice. 

If students successfully complete the practice problems, they can work on the College Project.  I have the projects and the College and University Fact Sheets ready in the back of the room.

If students are struggling, I may intervene in one of the following ways:

  • Ask them what their estimate is and how they got it.
  • Go back to the 1.2 x 0.05 strategies.  Ask them which one they feel most comfortable using and help them set up that strategy for a specific problem.
  • Give them a word problem situation that represents the problem.
  • Pull a small group of students who are struggling to work together.

Closure and Ticket to Go

10 minutes

I begin the Closure by asking students to look at questions 3 and 4.  What was your estimate? Why?  How did you find the exact product.  I look for students who used different strategies and I have them show and explain their work. If there is a common mistake I see students making, I will present it and ask students to address it here.

With about five minutes left I pass out the Ticket to Go for students to complete independently.  Then I pass out the HW Multiplying with Decimals Day 2. I may also assign one of the “Working During College” pages for homework, depending on how much students finished.